# Forwards in the debt markets

## Introduction

The forward market contracts that are found in the debt markets are:

• Forward interest rate contracts.

• Repurchase agreements.

• Forward rate agreements.

## Forward interest rate contracts

### Introduction

A forward interest rate contract (FIRC) is the sale of a debt instrument on a pre-specified future date at a pre-specified rate of interest. This category includes forwards on indices of interest rate instruments (such as forwards on the GOVI index). Below we provide examples of FIRCs in the OTC market and the exchange-traded markets:

• Example: OTC market.

• Examples: exchange-traded markets.

### Example: OTC market

An example is probably the best way to describe the forward market in interest rate products, i.e. forward interest rate contracts. As noted, these contracts involve the * sale of a debt instrument on a pre-specified future date at a pre-specified rate of interest, *and contain details on the following:

• The debt instrument/s.

• Amount of the instrument that will be delivered.

• Due date of the debt instruments.

• Forward date (i.e. due date of the contract).

• Rate of interest on the debt instrument to be delivered.

An insurance company requires a LCC100 million (plus) 206-day negotiable certificate of deposit (NCD) investment in 100 days' time when it receives a large interest payment. It wants to secure the rate now because it believes that rates on that section of the yield curve are about to start declining, and it cannot find a futures contract that matches its requirement in terms of the exact date of the investment (100 days from now) and its due date(306 days from now).

**Figure 5: example of forward interest rate contract**

It approaches a dealing bank and asks for a forward rate on LCC100 million (plus) 206-day NCDs for settlement 100 days from now. The spot rate (current market rate) on a 306-day NCD is 7.0% pa and the spot rate on a 100-day NCD is 5% pa. It will be evident that the dealing bank has to calculate the rate to be offered to the insurer from the existing rates. This involves the calculation of the rate * implied *in the existing spot rates, i.e. the

*(IFR) (see Figure 5):*

**implied forward rate**where

irL = spot interest rate for the longer period (306 days)

irS = spot interest rate for shorter period (100 days)

tL = longer period, expressed in days / 365) (306 / 365)

tc = shorter period, expressed in days / 365) (100 / 365)

IFR = {[1 + (0.07 x 306 / 365)] / [1 + (0.05 x 100 / 365)] -1} x 365 / 206 = [(1.05868 / 1.01370) -1] x 365 / 206 = (1.04437 - 1) x 365 / 206 = 0.07862 = 7.862% pa.

The bank will quote a rate lower than this rate in order to make a profit. However, we assume here, for the sake of explication, that the bank takes no profit on the client. It undertakes to sell the NCDs to the insurer at 7.862% pa after 100 days.

The financial logic is as follows9: the dealing bank could buy a 306-day NCD from another bank and sell it under repo (have it "carried") for 100 days; the repo buyer will earn 5.0% pa for 100 days and the ultimate buyer, the insurer (the forward buyer) will earn the IFR of 7.862% pa for 206 days. The calculations follow:

1. The dealing bank buys LCC100 million 306 day NCDs at the spot rate of 7.0% pa. The interest = 7.0 / 100 x LCC100 000 000 x 306 / 365 = LCC5 868 493.15.

2. The maturity value (MV) of the investment = cash outlay + interest for the period = LCC100 000 000 + LCC5 868 493.15 = LCC105 868 493.15.

3. The bank has the NCDs "carried" for 100 days at the spot rate for the period of 5.0% pa. This means it sells the LCC100 million NCDs at market value (LCC100 million) for a period of 100 days at the market rate of interest for money for 100 days.

4. After 100 days, the bank pays the "carrier" of the NCDs interest for 100 days at 5.0% pa on LCC100 million = LCC100 000 000 x 5.0 / 100 x 100 / 365 = LCC1 369 863.01.

5. The bank now sells the NCDs to the insurer at the IFR of 7.862% pa. The calculation is: MV / [1 + (IFR / 100 x days remaining to maturity / 365)] = LCC105 868 493.15 / [1 + (7.862 / 100 x 206 / 365)] = LCC101 370 498.00.

6. The insurer earns MV - cash outlay for the NCDs = LCC105 868 493.15 - LCC101 370 498.00 = LCC4 497 995.10 for the period.

7. Converting this to a pa interest rate: [(interest amount to be earned / cash outlay) x (365 / period in days)] = [(LCC4 497 995.10 / LCC101 370 498.00) x (365 / 206)] = 7.862% pa, i.e. the agreed rate in the forward contract.

Essentially what the dealing bank has done here is to hedge itself on the forward rate quoted to the insurer. It will be evident, however, that the bank, while hedged, makes no profit on the deal. As noted, in real life the bank would quote a forward rate lower than the break-even rate of 7.862% pa (e.g. 7.7% pa.)

The principle involved here, i.e. "carry cost" (or "net carry cost" in the case of income earning securities), is applied in all forward and futures markets. This will become clearer as we advance through this text.

The above is a typical example of a forward deal in the debt market. It will be apparent that the deal is a private agreement between two parties and that the deal is not negotiable (marketable). The market is not formalised and the risk lies between the two parties. It is for this reason that the forward interest rate contract market is the * domain of the large players, *and these are the large banks, and the institutions10.

Numbers in respect of OTC FIRCs are not available.